The bleach will fade the color of the roof and bleaches the dirt, not eliminate it. Bleach does not retard the re-growth of algae and mold. It will rust metal gutter systems and will leave drip marks on metal roofing and gutters. The high pressure can damage your roofing system.
A mold expert who comprehend mold development will make use of a non-toxic, biodegradable, USDA approved product. They will not use bleach or acid. The product is safe for children, plants, and animals. It is environmentally safe. It will retard the re-growth of mold, fungus and algae. It will not rust gutter systems or leave drip marks.
The item does most of the work and cleans into the pores of the concrete roofing material, the wood shake, and the asphalt singles. It is then rinsed with a reduced volume low pressure rinse system. Metal roofs can also be cleaned with the exact same system. You might wish to work with a mold professional who understands mold and cleans outside mold including roofs.